CHAPTER 11—COMPARISONS INVOLVING PROPORTIONS AND A TEST
Question
41. Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration.
Major
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Top Management
Middle Management
TOTAL
Management
280
220
500
Marketing
120
80
200
Accounting
150
150
300
TOTAL
550
450
1000
We want to determine if the position in management is independent of field (major) of concentration.
a.
Compute the test statistic.
b.
Using the p-value approach at 90% confidence, test to determine if management position is independent of major.
c.
Using the critical value approach, test the hypotheses. Leta = 0.10.
42. From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations. We are interested in determining if the selection of a TV station is independent of the level of education.
Educational Level
High School
Bachelor
Graduate
TOTAL
Public Broadcasting
50
150
80
280
Commercial Stations
150
250
120
520
TOTAL
200
400
200
800
a.
State the null and the alternative hypotheses.
b.
Show the contingency table of the expected frequencies.
c.
Compute the test statistic.
d.
The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
e.
Determine the p-value and perform the test.
43. Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store’s credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store’s credit card; 43 used a major credit card; and 61 paid cash. Witha = 0.05, test to see if the methods of payment have changed during the Christmas rush.
ANS:
.gif”>2 = 3.72; p-value (0.1557) is larger than 0.10; do not reject Ho; no change (critical .gif”>2 = 5.991)
PTS: 1 TOP: Hypothesis Testing
44. Dr. Sheryl Orr’s diet pills are supposed to cause significant weight loss. The following table shows the results of a recent study where some individuals took the diet pills and some did not.
Diet Pills
No Diet Pills
Total
No Weight Loss
80
20
100
Weight Loss
100
100
200
Total
180
120
300
We want to see if losing weight is independent of taking the diet pills.
a.
Compute the test statistic.
b.
Using the p-value approach at 95% confidence, test to determine if weight loss is independent on taking the pill.
c.
Use the critical method approach and test for independence.
45. A group of 500 individuals were asked to cast their votes regarding a particular issue of the Equal Rights Amendment. The following contingency table shows the results of the votes:
Sex
Favor
Undecided
Oppose
TOTAL
Female
180
80
40
300
Male
150
20
30
200
TOTAL
330
100
70
500
Ata = .05 using the p-value approach, test to determine if the votes cast were independent of the sex of the individuals.
46. Two hundred fifty managers with degrees in business administration indicated their fields of concentration as shown below.
Major
Top Management
Middle Management
TOTAL
Management
65
60
125
Marketing
30
20
50
Accounting
25
50
75
TOTAL
120
130
250
Ata = .01 using the p-value approach, test to determine if the position in management is independent of the major of concentration.
47. From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations.
Level of Education
High School
Bachelor
Graduate
TOTAL
Public Broadcasting
110
190
100
400
Commercial Stations
80
220
100
400
TOTAL
190
410
200
800
Test ata = .05 to determine if the selection of a TV station is dependent upon the level of education. Use the p-value approach.
48. The data below represents the fields of specialization for a randomly selected sample of undergraduate students. We want to determine whether there is a significant difference in the fields of specialization between regions of the country.
Northeast
Midwest
South
West
Total
Business
54
65
28
93
240
Engineering
15
24
8
33
80
Liberal Arts
65
84
33
98
280
Fine Arts
13
15
7
25
60
Health Sciences
3
12
4
21
40
150
200
80
270
700
a.
Determine the critical value of the chi-squarec2 for this test of independence.
b.
Calculate the value of the test statistic.
c.
What is the conclusion for this test? Leta = .05.